Annual rainfall maps for the Horizons-Manawatu Region

NIWA Client Report: WLG2008 / 69 November 2008 NIWA Project: ELF09201 / HZLC60

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Annual rainfall maps for the Horizons-Manawatu Region Andrew Tait James Sturman

Prepared for

Horizons Regional Council NIWA Client Report: WLG2008 / 69 November 2008 NIWA Project: ELF09201 / HZLC60 National Institute of Water & Atmospheric Research Ltd 301 Evans Bay Parade, Greta Point, Wellington Private Bag 14901, Kilbirnie, Wellington, New Zealand Phone +64-4-386 0300, Fax +64-4-386 0574 www.niwa.co.nz

Contents

1. Introduction 1

2. Spatial interpolation method 1

3. Annual rainfall maps for the Horizons-Manawatu Region 4

4. References 10

5. Appendix – Envirolink Fund Contract 12

Reviewed by: Approved for release by:

Alan Porteous David Wratt

Formatting checked

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Annual rainfall maps for the Horizons-Manawatu Region 1

1. Introduction

Horizons Regional Council (HRC) contracted NIWA (through the Envirolink fund – see appendix) to produce four maps of the annual rainfall for the Horizons-Manawatu Region (see location map, Figure 1). The four maps are the mean and median annual rainfall total (in millimeters) for the two overlapping 30-year periods 1971–2000 and 1978–2007. Geographic Information Systems (GIS) raster data grids at 500m spatial resolution (from which the maps are derived) have also been provided to HRC.

The period 1971–2000 was chosen because it is the latest climate “normal” period (the next normal period will be 1981–2010). As this period does not include recent years (which include some years with anomalously high and low rainfalls), the “most recent” 30-year period was also analysed and mapped, being the years 1978–2007.

This report briefly describes the spatial interpolation method used to produce the GIS data grids (and hence maps). Significantly, the interpolations used all the available annual rainfall data currently archived in the NIWA National Climate Database (clidb) for New Zealand plus additional annual rainfall data (not housed in clidb) supplied by HRC (see Figure 1).

2. Spatial interpolation method

The underlying usefulness of spatial interpolation methods is directly related to the quality and quantity of the surface observations. In New Zealand there is an excellent and extensive network of currently-open climate stations that record rainfall totals every day. The majority of these rainfall data are stored in the National Climate Database (clidb), an Oracle relational database. This is maintained by the National Institute of Water and Atmospheric Research (NIWA) in Wellington.

The two most successful methods used for the spatial interpolation of climate variables from surface observations covering large areas and encompassing complex terrain are kriging (including cokriging) and splines (Hutchinson and Gessler, 1994). Other methods such as inverse distance weighting, trend surface analysis (including linear and polynomial regression), and nearest neighbour tend to produce greater prediction errors in these situations, particularly those methods that do not include elevation information (Hutchinson and Bischof, 1983; Laslett et al., 1987, Phillips et al., 1992).

Annual rainfall maps for the Horizons-Manawatu Region 2

Figure 1: Extent of the Horizons-Manawatu region and the location of rainfall observations sites (data held in the NIWA climate database = blue circles; data held by Horizons Regional Council = green circles) used in the analysis.

Annual rainfall maps for the Horizons-Manawatu Region 3

Kriging and splines have many similarities (Matheron, 1981), and when the kriging variogram is well chosen, the prediction errors from both methods are similar (Seaman and Hutchinson, 1985; Laslett et al., 1987). A significant advantage of thin plate smoothing splines over kriging, however, is in their efficiency. Kriged surfaces are defined by minimizing the variance of the error of estimation, which normally depends on a preliminary variogram analysis. The accuracy of the fitted variogram model is a function of the correct selection of the variogram parameters and of the nugget variance in particular, which has a direct impact on the error properties of the fitted surface. The selection of these parameters often requires several trials, and the estimates are not always reliable (Hutchinson and Gessler, 1994).

A thin-plate smoothing spline works by fitting a surface to the data with some error allowed at each data point, so the surface can be smoother than if the data were fitted exactly. Each station is omitted in turn from the estimation of the fitted surface and the mean error is found. This is repeated for a range of values of a smoothing parameter, then the value that minimises the mean error is taken to give the optimum smoothing. This process is called minimizing the generalised cross validation (GCV). It can be automated once the order of the derivative, which controls the surface roughness, has been chosen.

The density of the observation network is the primary deficiency for interpolation methods. In lowland areas with relatively uncomplicated terrain (i.e. where the majority of the population reside) there is an abundance of rainfall data. On the other hand, rainfall observations in areas of mountainous terrain are often sparse and records are often relatively short with many missing values. This is not uncommon for many areas around the world (and is also the case for the Horizons-Manawatu Region, see Figure 1). Interpolation of rainfalls into these areas based on data from lower elevation stations sometimes several kilometres away can cause significant discrepancies.

In this study, we have chosen a thin plate smoothing spline model, which has been shown to perform well for the interpolation of New Zealand climate data (Sansom and Thompson, 2003; Tait et al., 2006; Tait and Turner, 2005; and Zheng and Basher, 1995). The software used was ANUSPLIN version 4.3 (Hutchinson, 2008).

Most meteorological variables, including rainfall, are affected by orography. Thus it makes sense to interpolate rainfall using a spline model with two position variables and an orographic variable such as elevation. The broad spatial pattern is determined by the two position variables, while the inclusion of elevation modifies the broad pattern to give more precise representations of the higher resolution variability.

Annual rainfall maps for the Horizons-Manawatu Region 4

Hutchinson (1995) used a trivariate thin plate smoothing spline (latitude, longitude, and elevation) to interpolate mean annual rainfall (and other meteorological variables) across Australia. A trivariate spline, which allows the relationship between rainfall and elevation to vary spatially, was deemed more appropriate for a continent-wide interpolation, compared with a trivariate partial spline (includes a single linear dependence upon elevation), which is more suited to small-scale applications.

To improve the interpolations further, we used a digitised version of a hand-drawn map of the mean annual rainfall for the period 1951–80, instead of elevation, in the trivariate spline model. The hypothesis was based on the observation that the 1951–80 map showed more realistic rainfall totals in the mountains (based on short-term observations, some high resolution NWP model runs, and observed river flows) than those produced from the elevation-based spline model. Last, we assigned a relative variance to each rainfall observation site, based on the inverse of the number of complete years of data. This relative variance weights stations with long records more strongly in the interpolation than stations with short records. Note that only sites with three or more years of data were included in the analysis.

Using this modelling approach, Figure 2 shows the median annual rainfall map for all of New Zealand and includes details of an interpolation error analysis performed at the observation sites. Note that this analysis is based on data sourced from clidb only. It can be seen that the mean prediction standard error over all the observation sites is 147.9 mm (note – at low elevation locations where there is a dense network of observation sites, the error is closer to the minimum value of 132.6 mm). The model prediction standard error is a combination of the variance of the data values and the model standard error estimate of the interpolated values.

Confidence intervals of the calculated spline values can be estimated by multiplying the prediction standard error by 1.96, the 95 percent two-sided confidence interval of the standard normal distribution.

3. Annual rainfall maps for the Horizons-Manawatu Region

Using annual rainfall data sourced from clidb and HRC, spline interpolations were performed on four datasets: the mean and median annual rainfall for the two periods 1971–2000 and 1978–2007. The GIS-formated output grids (provided to HRC) have a spatial resolution of 500m and are projected onto the New Zealand Map Grid. Figures 3–6 show the rainfall maps associated with these four data grids.

Annual rainfall maps for the Horizons-Manawatu Region 5

Figure 2: Interpolated median annual rainfall (based on the period 1971–2000) for all of New Zealand and an analysis of the interpolation error at the observation sites.

Annual rainfall maps for the Horizons-Manawatu Region 6

Figure 3: Interpolated mean annual rainfall (based on the period 1971–2000) for the Horizons-Manawatu region.

Annual rainfall maps for the Horizons-Manawatu Region 7

Figure 4: Interpolated median annual rainfall (based on the period 1971–2000) for the Horizons-Manawatu region.

Annual rainfall maps for the Horizons-Manawatu Region 8

Figure 5: Interpolated mean annual rainfall (based on the period 1978–2007) for the Horizons-Manawatu region.

Annual rainfall maps for the Horizons-Manawatu Region 9

Figure 6: Interpolated median annual rainfall (based on the period 1978–2007) for the Horizons-Manawatu region.

Annual rainfall maps for the Horizons-Manawatu Region 10

4. References

Hutchinson, M.F., 1995. Interpolating mean rainfall using thin plate smoothing splines. International Journal of Geographic Information Systems, 9, 385–403.

Hutchinson, M.F., 2008. ANUSPLIN, http://cres.anu.edu.au/outputs/anusplin.php. Last accessed October 2008.

Hutchinson, M.F. and Bischof, R.J., 1983. A new method for estimating the spatial distribution of mean seasonal and annual rainfall applied to the Hunter Valley, New South Wales. Australian Meteorological Magazine, 31, 179–184.

Hutchinson, M.F. and Gessler, P.E., 1994. Splines – more than just a smooth interpolator. Geoderma, 62, 45–67.

Laslett, G.M., McBratney, A.B., Pahl, P.J., and Hutchinson, M.F., 1987. Comparison of several spatial prediction methods for soil pH. Journal of Soil Science, 38, 325–341.

Matheron, G., 1981. Splines and kriging: their formal equivalence. Syracuse University Geological Contributions, 8, 77–95.

Philips, D.L., Dolph, J. and Marks, D., 1992. A comparison of geostatistical procedures for spatial analysis of precipitation in mountainous terrain. Agricultural and Forest Met., 58, 119–141.

Sansom, J. and Thompson, C.S., 2003. Mesoscale spatial variation of rainfall through a hidden semi-Markov model of breakpoint data. Journal of Geophysical Research, 108, D8, 8379, doi:10.1029/2001JD001447.

Seaman, R.S. and Hutchinson, M. F., 1985. Comparative real data tests of some objective analysis methods by withholding observations. Australian Meteorological Magazine, 33, 37–46.

Tait, A.B. and Turner, R.W., 2005. Generating multi-year gridded daily rainfall over New Zealand. Journal of Applied Meteorology, 44, 1315–1323.

Annual rainfall maps for the Horizons-Manawatu Region 11

Tait, A., Henderson, R. Turner, R. and Zheng, X., 2006. Thin-plate smoothing spline interpolation of daily rainfall for New Zealand using a climatological rainfall surface. International Journal of Climatology, 26, 2097-2115.

Zheng, X. and Basher, R., 1995. Thin-plate smoothing spline modelling of spatial climate data and its application to mapping South Pacific rainfalls. Mon. Wea. Review, 123, 3086–3102.

Annual rainfall maps for the Horizons-Manawatu Region 12

5. Appendix – Envirolink Fund Contract

Annual rainfall maps for the Horizons-Manawatu Region 13

Annual rainfall maps for the Horizons-Manawatu Region 14